We mention however that there is one caveat when ignoring the factor \(n^{o(1)}\)  in our above discussion. This is achieved by choosing the order \(p\)  of Trotterization sufficiently large, which can result in a gate complexity with an unrealistically large prefactor depending on the definition of higher-order formulas.For the \(p\) th-order Suzuki formula, we have a factor of \(5^p\)  in the gate complexity, although this may be different for different formulas. Nevertheless, recent work suggests that Trotterization remains advantageous for simulating the plane-wave-basis electronic structure even with a low-order formula [1]}, to which our paper provides new theoretical insights.
